Coherent Control of the Goos-H\"{a}nchen Shift in Polariton Optomechanics

TL;DR

This paper presents a theoretical method to control the Goos-H"{a}nchen} shift in a polariton optomechanical system using exciton-vibration interactions, enabling tunable beam displacement effects for advanced optical device design.

Contribution

It introduces a novel theoretical scheme for manipulating the GHS in polariton optomechanics via exciton-vibration coupling and system parameters.

Findings

Effective exciton-vibration coupling suppresses GHS at resonance.

Cavity detuning and length are tunable parameters for GHS control.

Increasing collective exciton-optical coupling enhances the GHS.

Abstract

We propose a theoretical scheme for controlling the Goos-H\"{a}nchen shift (GHS) of a reflected probe field in a polariton optomechanical system. The system comprises an optical mode, a molecular vibrational mode, and $N$ excitonic modes, where excitons couple to molecular vibrations via conditional displacement interactions and to photons through electric dipole interactions. We show that the effective exciton-vibration coupling provides a powerful mechanism for coherent GHS control: in its absence, the system exhibits a pronounced GHS at resonance, while activating it strongly suppresses the shift. The effective cavity detuning and the cavity length serve as additional tunable parameters for GHS manipulation. Furthermore, increasing the collective exciton-optical coupling enhances the GHS. Our results establish a framework for probing the GHS in polariton optomechanical systems and offer new avenues for designing optical devices that exploit beam-displacement phenomena.